Question

Estimate the value of $\cos 2\mathrm{\pi }?$

Answer 1

$\mathrm{\pi }$ is denoted for $180°$, which is half of the rotation of a unit circle.

Hence, $2\mathrm{\pi }$ denotes full rotation.

So, for any number of a full rotation, $n$ the value of $\cos$ will remain equal to $1$

we know that, $\cos \left(0°\right)=1$

Now, once we take a complete rotation in a unit circle, we reach back to the starting point.

After completing one rotation, the value of the angle is $360°$ or $2\mathrm{\pi }$ in radians.

Thus, we can say, after reaching the same position,

$\cos \left(0°\right)=\cos \left(360°\right)$

Or

$\cos \left(0°\right)=\cos \left(2\mathrm{\pi }\right)$

$\therefore cos(360°)=\cos \left(2\pi \right)=1$

Hence, $\cos 2\mathrm{\pi }=1$